Optical Bragg, atomic Bragg and cavity QED detections of quantum phases and excitation spectra of ultracold atoms in bipartite and frustrated optical lattices

► Develop a systematic and unified theory of various scattering experiments. ► Discuss the optical Bragg, atomic Bragg and cavity QED detection methods. ► Explore the detections of various quantum phases in various kinds of optical lattices. ► Present the detections of valence bond order and the supersolid order. ► Contrast the scattering methods with the in situ measurement.